Modelling a lever system¶
In this example, we implement a lever gear using physical modelling blocks.
Lever systems¶
Many mechanisms have levers in their composition: bicycle brakes and floor scales, piano hammers, the mechanism for lifting the body of a dump truck or the boot of a car, hydraulic platforms and lever gears in car brakes.
They are often assembled into lever systems, or lever gears, and which may contain several levers, arms, linkages, hangers, pivots and other mechanical elements.
In this example, a model of such a device will allow us to know what displacement or output force is produced by a lever system comprising levers of the first, second and third kind.
Model description¶
In this example we show the operation of the block Lever (lever). Four levers are involved in the process:
- The first (
Lever 1) and the fourth (Lever 4) are levers of the second kind, their fulcrum is at one end of the lever bar. The force is applied to the other end of the crossbar and the load is placed in the middle - The third lever (
Level 3) is a lever of the first kind, its fulcrum is at the centre, between the force and the load. - The second lever (
Lever 2) summarises the work of all the others.
The diagram above shows a speculative mechanism. Besides levers, it contains dampers, springs and two mass blocks. Since we have just a model of the dynamics and kinematics of some part of the modelled mechanism, the mass blocks Mass can be ordinary masses placed directly on the levers, or they can model aerodynamic loads. The same applies to the sources of force - they can be models of the impact that the pilot exerts on the control pedals along the aircraft's course, or models of any other interaction.
The opsane mechanism is affected by two forces that start to act at different moments of time. At t=1 s, a force of 100 N is applied to the free end of the lever Lever 1. Then, at t=2 s, a force of 200 N is applied to the bar end of the lever Lever 3.
Running the model¶
Let's start the model using [programme control] commands(https://engee.com/helpcenter/stable/modeling/programmatic-modeling.html).
In [ ]:
modelName = "linkage_mechanism"
model = modelName in [m.name for m in engee.get_all_models()] ? engee.open( modelName ) : engee.load( "$(@__DIR__)/$modelName.engee" );
model_data = engee.run( modelName )
Out[0]:
Dict{String, DataFrame} with 1 entry:
"out" => 401×2 DataFrame…
In [ ]:
plot( model_data["out"].time, hcat(model_data["out"].value...)' )
Out[0]:
As expected, we see the effect of two disturbing influences.
Conclusion¶
The Engee physical modelling blocks allow the modelling of various mechanisms, and due to the graphical nature of these models, the user can spend less time composing equations, and more time on system analysis, requirements elicitation and designing a model environment for our development.
Blocks used in example¶
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